normalizing constant from kernel density in R

Question

How can I get the normalizing constant from a non-standard distribution. Ex:

x <- c(rnorm(500,10,1),rnorm(500,20,2),rnorm(500,35,1))

after using density in R

dens<-density(x,n=length(x),adjust=0.4)

Answer 1

The result of density() should be a proper probability density function, so the area under the curve returned by density() should already be 1.

Your example:

set.seed(1)
x <- c(rnorm(500,10,1), rnorm(500,20,2), rnorm(500,35,1))
dens <- density(x, n=length(x), adjust=0.4)

We can get an approximation of the area under the pdf by numerically integrating it:

install.packages("sfsmisc")
library(sfsmisc)
integrate.xy(dens$x, dens$y)

Which gives

[1] 1.000241

The area is indeed rather close to 1.

There are numerical accuracy issues however which may cause this area to deviate significantly from 1. They are discussed here for example.